Question

Find the mean, μ, and standard deviation, σ, for a binomial random variable X. (Round all answers for σ to three decimal places.)

(a) n = 20, p = .50.

μ =

σ =

(b) n = 1, p = 0.35.

μ =

σ =

(c) n = 100, p = 0.80.

μ =

σ =

(d) n = 30, p = .01.

μ =

σ =

Answer 1

Solution :

Given that,

p = 0.50

q = 1 - p =1-0.50=0.50

n = 20

Using binomial distribution,

Mean = = n * p = 20*0.50=10

Standard deviation = = n * p * q =  20*0.50*0.50=2.236

(B)

p = 0.35

q = 1 - p =1-0.35=0.65

n = 1

Using binomial distribution,

Mean = = n * p = 1*0.35=0.35

Standard deviation = = n * p * q =  1*0.35*0.65=0.477

)C)

p = 0.80

q = 1 - p =1-0.80=0.20

n = 100

Using binomial distribution,

Mean = = n * p = 100*0.80=80

Standard deviation = = n * p * q =  100*0.80*0.20=4

(D)

p = 0.01

q = 1 - p =1-0.01=0.99

n = 30

Using binomial distribution,

Mean = = n * p = 30*0.01=0.30

Standard deviation = = n * p * q =  30*0.01*0.99=0.545